Perfect number in gaussian integers We have complete description about irreducibles in the ring Z[i],of gaussian integers. Now I was trying to define suitably the notion of "perfect number" in Z[i]. But the problem is unique factorization into irreducibles is unique upto associates. So how one should possibly try to resolve this?

Well in the integers you don't mix positive and negative factors. Why not pick the/a sum of factors with the maximum modulus which would be compatible with the usual definition for integers.